Exam (elaborations)
MFP1501 ASSIGNMENT 3
- Course
- MFP1501 ASSIGNMENT 3
- Institution
- University Of South Africa
MFP1501 ASSIGNMENT 3
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A+MFP1501
ASSIGNMEN
T 3
This document contains
workings and solutions to
the question below
Admin
JIMMY COSMAS
, Question 1
In this MFP1501, we refer to mathematical modelling as the process whereby we use
abstractions of mathematics to solve problems in the real world. For example, there are 21
learners in Grade 5 that will go on an excursion to Zoo Lake. If one car will take a
maximum of 6 learners, how many cars do we need to carry everyone? You may use one
car to work out 21 divided by 6. This will give you 3,5. So, you would need 4 cars. Haylock
(2014) argues that there are four steps involved in this reasoning. In step 1, a problem in
the real world is translated into a problem expressed in mathematical symbols (21÷6, in
this case). In step 2, the mathematical symbol is manipulated to obtain a mathematical
solution (3,5). Step 3 is to interpret the mathematical solution back in the real world (3
cars, and a half). The final step is to check the answer against the constraints of the
original solution. In this case, since you cannot have half of a car, the appropriate
conclusion is that you need 4 cars. 1.1 Summarise the process of mathematical modelling
by first drawing a diagram similar to Figure 3.1 in the study guide. N. B it should not be the
same. Be creative. (8) 1.2 In each of the steps in your diagram make use of practical
examples that will translate into your scenario of using abstractions of mathematics to
solve problems in the real world. (15) 4
1. Step 1: Translating the real-world problem into mathematical symbols. Example:
Given that there are 21 learners and each car can carry a maximum of 6 learners,
we represent this as a division problem: 21 ÷ 6.
2. Step 2: Manipulating the mathematical symbols to find a solution. Example:
Solving the division problem, we find that 21 ÷ 6 = 3.5.
3. Step 3: Interpreting the mathematical solution back into the real world. Example:
Since we cannot have half a car, we interpret the solution as needing 4 cars to
carry all the learners.
4. Step 4: Checking the answer against the constraints of the original problem.
Example: By considering the constraint that each car can carry a maximum of 6
learners, we verify that with 4 cars, all 21 learners can be transported.
Question 2 As a mathematics teacher, you are expected to help children develop
multiplicative thinking, which goes beyond repeated addition, as it may not happen for
many learners. It is the intention of MFP1501 learning unit 4 to support you to do so.
Jacob and Willis (2003) outline hierarchical phases through which multiplicative thinking
develops, which include one-to-one counting, additive composition, many-to-one counting,
and multiplicative relations. 2.1 Describe each phase through which multiplicative thinking
develops. (20) 2.2 Motivate your descriptions in 2.1 with practical examples. (12)
2.1 Describe each phase through which multiplicative thinking develops:
1. One-to-One Counting: In the one-to-one counting phase, learners establish the
concept of counting objects one by one. They understand that each object
corresponds to one count, allowing them to determine the cardinality of a set. For
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